Propriedades e aspectos geométricos de estimadores tipo James-Stein e do estimador de Hartigan

The James-Stein estimator is a biased shrinkage estimator with uniformly smaller risk than the risk of the sample mean estimator for the mean of multivariate normal distribution, except in the one-dimensional or two-dimensional cases. In this work we have used more heuristic arguments and intensified the geometric treatment of the theory of James-Stein estimator. New type James-Stein shrinking estimators are proposed and the Mahalanobis metric used to address the James-Stein estimator. . To evaluate the performance of the estimator proposed, in relation to the sample mean estimator, we used the computer simulation by the Monte Carlo method by calculating the mean square error. The result indicates that the new estimator has better performance relative to the sample mean estimator.

Risco de crédito: uma abordagem utilizando análise discriminante, regressão logística e redes neurais artificiais

Considering the relevance of researches concerning credit risk, model diversity and the existent indicators, this thesis aimed at verifying if the Fleuriet Model contributes in discriminating Brazilian open capital companies in the analysis of credit concession. We specifically intended to i) identify the economic-financial indicators used in credit risk models; ii) identify which economic-financial indicators best discriminate companies in the analysis of credit concession; iii) assess which techniques used (discriminant analysis, logistic regression and neural networks) present the best accuracy to predict company bankruptcy. To do this, the theoretical background approached the concepts of financial analysis, which introduced themes relative to the company evaluation process; considerations on credit, risk and analysis; Fleuriet Model and its indicators, and, finally, presented the techniques for credit analysis based on discriminant analysis, logistic regression and artificial neural networks. Methodologically, the research was defined as quantitative, regarding its nature, and explanatory, regarding its type. It was developed using data derived from bibliographic and document analysis. The financial demonstrations were collected by means of the Economática ® and the BM$FBOVESPA website. The sample was comprised of 121 companies, being those 70 solvents and 51 insolvents from various sectors. In the analyses, we used 22 indicators of the Traditional Model and 13 of the Fleuriet Model, totalizing 35 indicators. The economic-financial indicators which were a part of, at least, one of the three final models were: X1 (Working Capital over Assets), X3 (NCG over Assets), X4 (NCG over Net Revenue), X8 (Type of Financial Structure), X9 (Net Thermometer), X16 (Net Equity divided by the total demandable), X17 (Asset Turnover), X20 (Net Equity Profitability), X25 (Net Margin), X28 (Debt Composition) and X31 (Net Equity over Asset). The final models presented setting values of: 90.9% (discriminant analysis); 90.9% (logistic regression) and 97.8% (neural networks). The modeling in neural networks presented higher accuracy, which was confirmed by the ROC curve. In conclusion, the indicators of the Fleuriet Model presented relevant results for the research of credit risk, especially if modeled by neural networks.

Estabilidade e adaptabilidade de híbridos de milho utilizando a abordagem AMMI-bayesiano

Biplot graphics are widely employed in the study of the genotypeenvironment interactions, but they are only a graphical tool without a statistical hypothesis test. The singular values and scores (singular vectors) used in biplots correspond to specific estimates of its parameters, and the use of uncertainty measures may lead to different conclusions from those provided by a simple visual evaluation. The aim of this work is to estimate the genotype-environment interactions, using AMMI analysis, through Bayesian approach. Therefore the credibility intervals can be used for decision-making in different situations of analyses. It allows to verify the consistency of the selection and recommendation of cultivars. Two analyses were performed. The first analysis looked into 10 regular commercial hybrids and all possible 45 hybrids obtained from them. They were assessed in 15 locations. The second analysis evaluated 28 hybrids in 35 different environments, with imbalance data. The ellipses were grouped according to the standard of interaction in the biplot. The AMMI analysis with a Bayesian approach proved to be a complete analysis of stability and adaptability, which provides important information that may help the breeder in their decisions. The regions of credibility, built in the biplots, allow to perform an accurate selection and a precise genotype recommendation, with a level of credibility. Genotypes and environments can be grouped according to the existing interaction pattern, which makes possible to formulate specific recommendations. Moreover the environments can be evaluated, in order to find out which ones contribute similarly to the interaction and those to be discarted. The method makes possible to deal with imbalanced data in a natural way, showing efficiency for multienvironment trials. The prediction takes into account instability and the interaction standard of the observed data, in order to establish a direct comparison between genotypes of both 1st and 2nd seasons.